mul_le_one — Mathlib

English

If a ≤ 1 and b ≤ 1 in a preorder monoid with right monotone multiplication, then a·b ≤ 1.

Русский

Если a ≤ 1 и b ≤ 1 в предельно-порядковом моноиде с правой монотонностью умножения, то a·b ≤ 1.

LaTeX

$$$\forall a,b\in \alpha\; (a \le 1) \to (b \le 1) \Rightarrow a b \le 1$$$

Lean4

/-- Assumes right covariance.
The lemma assuming left covariance is `Left.mul_le_one`. -/
@[to_additive /-- Assumes right covariance.
    The lemma assuming left covariance is `Left.add_nonpos`. -/
    ]
theorem mul_le_one [MulRightMono α] {a b : α} (ha : a ≤ 1) (hb : b ≤ 1) : a * b ≤ 1 :=
  mul_le_of_le_one_of_le ha hb

Похожие утверждения